MT-SGD samples from multiple target distributions using gradient descent.
problem Sampling from multiple unnormalized target distributions.
method Proposes MT-SGD, a flow of intermediate distributions to sample from multiple target distributions.
result Asymptotic analysis shows MT-SGD reduces to multiple-gradient descent for multi-objective optimization.
Gradient descent struggles to achieve zero loss in deep learning models due to non-generic data distributions.
problem Achieving zero loss minimizers in deep learning networks.
method Analysis of gradient descent algorithm in deep learning, focusing on underparametrized networks.
result Zero loss minimization cannot be achieved generically in deep learning networks.
ErasureHead speeds up distributed GD with approximate gradient coding.
problem Mitigating delays in distributed gradient descent.
method Approximate gradient coding to tolerate delays.
result ErasureHead converges as quickly as GD and has faster runtime under probabilistic delays.
The paper examines how SGD noise deviates from Gaussian distribution.
problem Understanding why SGD outperforms GD in neural networks.
method Analysis of SGN vectors' distribution during training.
result For large batch sizes, SGN vectors are mostly Gaussian in early phases.
Gradient descent finds halfspaces with low error for agnostic learning.
problem Agnostic learning of linear halfspaces with convex surrogates.
method Gradient descent on convex surrogates for zero-one loss.
result Gradient descent finds halfspaces with error O(OPT1/2+ε) in poly time and sample complexity. BSVGD improves sampling for multimodal distributions using branching.
problem Sampling from multimodal distributions.
method Random branching in Stein Variational Gradient Descent (SVGD).
result Theoretical convergence guarantee and empirical validation.
The paper studies stochastic gradient descent with infinite variance gradients.
problem Theoretical properties of SGD with infinite variance gradients.
method Establish asymptotic behavior of SGD with infinite variance gradients.
result Asymptotic distribution of SGD is characterized as a stationary distribution of an Ornstein-Uhlenbeck process driven by a stable Lévy process.
A new method for sampling high-dimensional distributions overcomes overfitting.
problem Overfitting in energy-based models during gradient descent.
method Mean-field microcanonical gradient descent, which samples multiple data points simultaneously.
result The method reduces entropy loss while maintaining likelihood fit, improving overfitting issues.
Gradient descent on MMD GAN parameter space converges globally to target distribution.
problem Convergence of gradient descent in Maximum Mean Discrepancy (MMD) GANs.
method Proposes a parametric kernelized gradient flow that mimics the min-max game in gradient regularized MMD GAN.
result Gradient descent on the generator's parameter space in gradient regularized MMD GAN is globally convergent to the target distribution under certain conditions.
Gradient descent learns ReLU functions with non-zero bias efficiently.
problem Learning ReLU functions with non-zero bias under Gaussian distributions.
method Gradient descent starting from random initialization.
result Gradient descent achieves near-optimal error with high probability.
This work proposes a new method for variational inference using Wasserstein gradient descent.
problem Optimizing variational parameters to match a true posterior distribution.
method Reinterpreting VI as an optimization problem over a variational parameter space, using Wasserstein gradient descent.
result The proposed Wasserstein gradient descent can be seen as a generalization of existing optimization techniques in VI.
This paper analyzes Stein variational gradient descent for Bayesian inference.
problem Sampling or approximating high-dimensional probability distributions.
method Iterated steepest descent steps with a reproducing kernel Hilbert space norm.
result Performance gains of certain nondifferentiable kernels with adjusted tails.
Gradient equilibrium improves online learning performance without requiring sublinear regret.
problem Achieving sublinear regret in online learning.
method Gradient equilibrium: average of gradients converges to zero.
result Gradient equilibrium can be achieved by standard online learning methods.
Gradient descent fails to learn simple neural networks efficiently.
problem Learning one-layer neural networks efficiently using gradient descent.
method Gradient descent and statistical query algorithms.
result Superpolynomial lower bounds for learning one-layer neural networks.
Paper proposes a pre-conditioning technique to speed up gradient-descent convergence in distributed linear least-squares problems.
problem Expediting convergence of gradient-descent method for ill-conditioned distributed linear least-squares problems.
method Iterative pre-conditioning technique to improve convergence rate of gradient-descent method.
result Pre-conditioned gradient-descent achieves superlinear convergence for unique solutions and improved linear convergence otherwise.
Paper addresses fault-tolerance in distributed machine learning with stochastic gradient descent.
problem Fault-tolerance in distributed stochastic gradient descent (D-SGD) for machine learning.
method Proposes norm-based comparative gradient elimination (CGE) to robustify D-SGD against Byzantine faulty agents.
result CGE guarantees fault-tolerance against a bounded fraction of Byzantine agents under standard stochastic assumptions.
Proposes variance reduction for optimizing permutation models.
problem High variance in gradient estimates for discrete latent variables.
method Control variates for the Plackett-Luce distribution.
result Optimization of black-box functions over permutations using SGD.
Paper proposes a pre-conditioning method to speed up gradient descent in multi-agent optimization.
problem Speed up convergence of gradient descent in multi-agent optimization problems.
method Iterative pre-conditioning approach to mitigate the effect of problem conditioning.
result Significant improvement in convergence speed of gradient descent method.
SGD reduces test error by decorrelating updates.
problem Improving generalization error in machine learning models.
method Derive a formula for generalization gap change due to SGD updates, compare to GD, and show decorrelation effect.
result SGD implicitly regularizes generalization error by decorrelating updates.
Kalman Gradient Descent optimizes machine learning models by reducing variance in stochastic optimization.
problem Reducing variance in stochastic gradient descent to improve optimization performance.
method Uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent.
result Improved performance on various machine learning tasks including neural networks and black box variational inference.
Gradient descent fails to train two-layer ReLU networks, leading to poor performance.
problem Gradient descent training of two-layer ReLU networks initialized by He et al. (2015) fails to find optimal solutions.
method Gradient descent on a least-squares loss for training two-layer (Leaky)ReLU networks.
result Gradient descent only finds bad local minima, leading to linear regression for non-linear target functions.
New bounds for model generalization under deterministic gradient descent.
problem Establishing generalization bounds for models trained with gradient descent methods.
method PAC-Bayesian bounds for deterministic optimisation algorithms.
result Fully computable bounds that depend on initial distribution and Hessian.
Paper reduces communication in distributed machine learning.
problem Reduces burdensome communication in distributed machine learning.
method Introduces communication-censoring technique to reduce transmissions of variables.
result CSGD algorithm achieves same convergence rate as SGD but with significant communication reduction.
Gradient descent on DDPM objective learns Gaussian mixtures efficiently.
problem Learning Gaussian mixtures using gradient-based methods.
method Gradient descent on DDPM objective, connecting to EM and spectral methods.
result Gradient descent can efficiently recover Gaussian mixture parameters under certain conditions.
MWGraD solves multi-objective distributional optimization using particle-based gradient descent.
problem Simultaneously minimize multiple objective functionals over probability distributions.
method Iterative particle-based algorithm MWGraD, estimating and aggregating Wasserstein gradients.
result Demonstrates effectiveness on synthetic and real-world datasets.
Paper analyzes SVGD algorithm for non-asymptotic convergence.
problem Optimizing a set of particles to approximate a target probability distribution.
method Finite time analysis of SVGD algorithm, providing descent lemma and convergence rates.
result SVGD algorithm decreases the objective at each iteration and converges to the target distribution.
KSD Descent uses KSD to sample from a target distribution efficiently.
problem Sampling from complex target distributions efficiently.
method Wasserstein gradient flow of KSD, using L-BFGS optimization.
result KSD Descent can sample from a target distribution using a set of particles.
Two novel algorithms improve distributed machine learning in the presence of Byzantine adversaries.
problem Improving distributed machine learning in the presence of Byzantine adversaries.
method Two novel stochastic gradient descent algorithms, ByGARS and ByGARS++, using reputation scores for gradient aggregation.
result Robust to any number of multiplicative noise Byzantine adversaries and converge for strongly convex loss functions.
Distributed learning with random features and gradient descent improves performance and reduces memory usage.
problem Improving generalization in decentralized learning with limited memory.
method Distributed Gradient Descent with Random Features and Implicit Regularization.
result High probability bounds on predictive performance with optimal statistical rates.
A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.
problem Optimizing functionals over probability distributions using finite particle systems.
method Virtual particle stochastic approximation, viewed as a form of stochastic gradient descent in the Wasserstein space.
result The algorithm's output converges to the optimal distribution and produces i.i.d. samples.
New method optimizes SDE models using continuous-time gradient descent.
problem Optimizing over the stationary distribution of SDE models.
method Continuous-time stochastic gradient descent for SDE models.
result Asymptotic convergence to the direction of steepest descent.
Hybrid approach reduces computation time and decoding complexity.
problem Straggling servers in distributed computing.
method Coded partial gradient computation (CPGC) that balances gradient accuracy and completion time.
result Reduces both computation time and decoding complexity.
Gradient descent converges to minimum Bayes risk for two-layer ReLU networks in mean field regime.
problem Training two-layer ReLU networks using gradient descent in the mean field regime.
method Describes a condition for convergence to minimum Bayes risk, extending previous results to ReLU-activated networks.
result The condition for convergence does not depend on initialization and concerns weak convergence of network realization.
SVGD algorithm converges at rate 1/sqrt(log log n) for sub-Gaussian distributions.
problem Approximating a probability distribution with particles.
method Stein variational gradient descent (SVGD) with finite particles and sub-Gaussian target distribution.
result SVGD achieves a convergence rate of 1/sqrt(log log n) for sub-Gaussian distributions.
Distributed Gradient Descent achieves optimal rates in non-parametric regression with linear speed-up.
problem Optimal statistical rates in decentralized non-parametric regression.
method Distributed Gradient Descent with i.i.d. samples and linear speed-up.
result Achieves optimal statistical rates with linear speed-up in the big data regime.
WarpGrad efficiently learns preconditioning matrices for gradient descent across task distributions.
problem Learning efficient update rules for rapid new task learning.
method Interleaves warp-layers between task-learner layers to meta-learn preconditioning matrices.
result WarpGrad scales to large meta-learning problems and improves across various learning settings.
Gradient descent with random weights in linear regression analyzed for various noise types.
problem Analyzing the impact of random noise on gradient descent in linear regression.
method Gradient descent with randomly weighted data points, various weighting distributions, geometric moment contraction.
result Characterization of implicit regularization and non-asymptotic convergence bounds.
We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from τ rounds ago. First, we show that without stochastic noise, delays strongly affect the attainable optimization error: In fact, the error…
NVGD uses neural networks to infer distributions without kernel choices.
problem Challenges in choosing kernel functions for SVGD.
method NVGD parameterizes the witness function of the Stein discrepancy with a neural network.
result NVGD achieves good performance on various inference problems.
Law derived for neural networks with sparse connections.
problem Understanding the behavior of neural networks with sparse connections.
method Law of large numbers for empirical distribution of parameters derived.
result Law for neural networks with sparse connections derived.
A major challenge in understanding the generalization of deep learning is to explain why (stochastic) gradient descent can exploit the network architecture to find solutions that have good generalization performance when using high capacity models. We find simple but realistic examples showing that this phenomenon exis…
Distributed algorithm finds global solutions for low-rank matrices.
problem Finding global solutions for low-rank matrices in distributed systems.
method Distributed Gradient Descent (DGD+) with LOCAL variables.
result DGD+LOCAL converges to global minimizer with exact consensus.
This paper accelerates distributed convex optimization by mitigating ill-conditioning issues.
problem Distributed convex optimization with ill-conditioned aggregate cost functions.
method Iterative pre-conditioning technique to improve convergence rate and stability.
result The proposed algorithm converges linearly with improved convergence rate and superlinearly under certain conditions.
New dynamics for SGD in small learning rate regime.
problem Improving stochastic gradient descent in small learning rate regime.
method Introducing stochastic modified flows and distribution dependent stochastic modified flows.
result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.
SGD improves DR by solving two-stage sampling problems.
problem Improving the learning properties of SGD for distribution regression.
method Applying SGD to two-stage sampling problems in distribution regression.
result Theoretical guarantees for SGD's performance in DR, with optimal bounds.
A new method for learning Gaussian Mixture Models using gradient descent.
problem Learning Gaussian Mixture Models efficiently and with gradient descent.
method Sliced Cramér 2-distance for multivariate GMMs, compatible with gradient descent.
result Closed-form solution for univariate case, easy to implement.
Heavy-tailed distributions emerge in SGD's parameter evolution.
problem Understanding heavy-tailed distributions in SGD parameter evolution.
method Continuous diffusion approximation of SGD (homogenized SGD) analysis.
result Explicit upper and lower bounds on tail-index of homogenized SGD.
Study on privacy leakage in noisy gradient descent algorithms.
problem Information leakage of iterative randomized learning algorithms about training data.
method Analyzes the dynamics of Rényi differential privacy loss in noisy gradient descent algorithms.
result Privacy loss converges exponentially fast for smooth and strongly convex loss functions.